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• Mode I fracture process is characterized for GFRP-steel bi-material interface. • Double-cantilever beam experiments supplemented by detailed DIC measurement. • Accurate modeling of crack initiation, fiber bridging and propagation by new CZM. • Four-linear traction-separation law derived from DIC measurements and iterative FEA. Debonding is characterized as the governing failure mode in the innovative wrapped composite joints made with glass fiber composite material wrapped around steel hollow sections without welding. The prerequisite for predicting debonding failure of wrapped composite joints is to obtain fracture behavior of the composite-steel bonded interface. The mode I fracture behavior of the bonded interface was experimentally investigated using glass fiber composite-steel double cantilever beam (DCB) specimens. The crack length a and the crack tip opening displacement (CTOD) during the test were accurately measured by analyzing the digital image correlation (DIC) data while the strain energy release rate (SERR) was calculated through the extended global method (EGM). The cohesive zone modeling (CZM) was utilized in the finite element model with the proposal of a four-linear traction-separation law to simulate the mode I fracture process. An approach is introduced to determine the critical stages of the proposed four-linear cohesive law by combining accurate measurements of crack length a and CTOD, along with SERR values. The validity of the four-linear cohesive law and the introduced approach to determine the critical stages were confirmed by good agreement in both global and local behavior between the testing and the FEA results. [ABSTRACT FROM AUTHOR]